Unveiling Complex Collective Behaviors from Simple Rewards

Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution. We ask whether this leaves a measurable signature, geometric or behavioral, on learned representations. We propose EffRank/$n$ (effective rank normalized by agent count) and $D_\text{act}$ (mean pairwise KL divergence between agents' action distributions) as low-overhead diagnostics for reward-attribution effects, then test them on competent MAPPO agents in SMACv2 \texttt{protoss_5_vs_5}, where unit type is encoded in the observation. In an observation $\times$ reward-attribution comparison (unit type observed vs.\ masked; individual damage-contribution reward vs.\ shared team reward), geometry follows observation rather than reward. With unit type observed, shared and individual rewards have similar EffRank/$n$ ($0.31{\pm}0.03$ vs.\ $0.29{\pm}0.02$) and probe accuracy ($0.75{\pm}0.05$ vs.\ $0.73{\pm}0.05$, both $\gg 1/3$ chance), while $D_\text{act}$ leans higher under individual rewards ($1.23{\pm}0.06$ vs.\ $1.07{\pm}0.20$). Masking unit type cuts the above-chance probe signal by more than half, to $0.49$ in both reward arms. In short: individually rewarded agents are competent and separable by role, but on SMACv2 the observation explains the geometry and reward attribution shows up mainly in behavior. Thus geometric diagnostics must control for observed role information and test persistent roles that are not directly observed. EffRank/$n$ and $D_\text{act}$ add $<$5% overhead.

Sparse rewards are a major bottleneck in multi-agent reinforcement learning (MARL), where simultaneous learning induces non-stationarity and makes reward design especially delicate. Reward shaping can accelerate learning, but in the multi-agent setting it must preserve the strategic structure of the problem rather than merely improve short-term optimization. We propose Automatic Reward-shaping in Multi-agent Systems (ARMS), a self-supervised reward shaping framework for MARL that learns dense shaping signals from sparse environmental rewards through trajectory ranking. Since single-agent trajectory-ranking guarantees do not directly transfer to MARL, we reformulate policy invariance through conditional best-response reasoning, and show that if certain conditions hold, then using shaping rewards preserves each agent's best-response set under fixed opponent policies, and consequently preserve the set of Nash equilibria. Guided by this perspective, ARMS alternates between policy learning and reward learning while sharing shaping parameters across agents for efficiency. Experiments in a partially observable multi-agent pathfinding domain show that ARMS improves sampling efficiency under increasing reward sparsity and agent count, generalizes to unseen environments, and reveals a MARL-specific failure mode in which limited exploration and coupled policy--reward dynamics induce oscillatory behavior. Increasing exploration mitigates this effect and stabilizes learning. To the best of our knowledge, ARMS is the first automatic reward shaping framework for MARL whose design is motivated by a game-theoretic equilibrium-preservation result.

Multi-agent simulations are widely used to study complex social and ecological systems, where rich and often unexpected emergent behaviors arise from local interactions. A large body of prior work has focused on analyzing such emergent dynamics across domains. In this paper, we move beyond analyzing emergent behavior and introduce a learning-based mechanism for actively shaping it via social reward modeling. We introduce Multi-Agent Reward Prediction (MARP), a simple framework that extends preference-based reward modeling to multi-agent reinforcement learning. While the framework is designed to be applicable across multi-agent settings, the present empirical validation is limited to a single environment, and we therefore present MARP as a proof of concept within the studied domain. Rather than relying on handcrafted rewards, MARP learns a shared reward model from episode-level evaluations of collective outcomes, enabling decentralized agents to align their behavior with global social objectives. We study MARP in the Harvest Game, a canonical sequential social dilemma modeling common-pool resource management and related real-world challenges. Our results show that MARP can be tuned to produce behavior that is more closely aligned with target social metrics than standard reward-based baselines, while the learned reward model captures subtle environmental structure without explicit programming. Crucially, MARP supports multiple and composite social objectives within a single training regime. By modifying only the high-level evaluation metric, the same framework seamlessly aligns agent behavior with diverse goals, including sustainability, equality, and peace, as well as combinations of individual and group-level objectives. These findings demonstrate that emergent multi-agent behavior can be treated not only as a phenomenon to study, but as a target of principled, data-driven regulation.